In an isothermal process

Explanation

Isothermal process: It is a process in which the temperature remains constant but the pressure and volume of a thermodynamic system will change. The ideal gas equation is
`PV = muRT`
Here, T is constant for this process So the equation of state for isothermal process is given by
`"PV = Constant ...(1)"`
This implies that if the gas goes from one equilibrium state `(P_(1)V_(1))` to another equilibrium state `(P_(2)V_(2))` the following relation holds for this process
`(P_(1)V_(1))` = `(P_(2)V_(2))" …(2)"`
Since `"PV = constant,"` P is inversely proportional to `V(P prop (1)/(V))`. This implies that PV graph is a hyperbola. The pressure-volume graph for constant temperature is also called isotherm. We know that for an ideal gas the internal energy is a function of temperature only. For an isothermal process since temperature is constant, the internal energy is also constant. This implies that `dU or DeltaU = 0`.
For an isothermal process, the first law of thermodynamics can be written as,
`"Q = W …(3)"`

From equation (3), we infer that the heat supplied to a gas is used to do only external work, It is a common misconception that when there is flow of heat to the system, the temperature will increase. For isothermal process this is not true. The isothermal compression takes place when the piston of the cylinder is pushed. This will increase the internal energy which will flow out of the system through thermal contact.